Some new results on the Blaszak–Marciniak lattice: Bäcklund transformation and nonlinear superposition formula

Abstract

The so-called Blaszak–Marciniak lattice is considered. By the dependent variable transformation, the Blaszak–Marciniak lattice is transformed into a quart-linear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation is obtained. Furthermore, a nonlinear superposition formula is proved rigorously. As an application of the obtained results, soliton solutions are derived.